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Zero CR-curvature equations for Levi degenerate hypersurfaces via Pocchiola’s invariants
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 28 (2019) no. 5, pp. 957-976.

Dans nos articles précédents, nous avons étudié les hypersurfaces tubes dans l’espace euclidien complexe de dimension trois, qui sont 2-non-dégénérées et uniformément Levi dégénérées de rang 1. Nous avons montré en particulier que l’annulation de la courbure CR d’une telle hypersurface est équivalente à une équation de Monge par rapport à une des variables. Dans cet article nous dérivons cette équation par une approche alternative plus rapide, en utilisant deux invariants découverts par S. Pocchiola. Nous étudions également les invariants de Pocchiola dans le cas rigide et donnons une classification partielle des hypersurfaces rigides 2-non-dégénérées uniformément Levi dégénérées de rang 1 à courbure CR nulle.

In articles [8, 9] we studied tube hypersurfaces in 3 that are 2-nondegenerate and uniformly Levi degenerate of rank 1. In particular, we showed that the vanishing of the CR-curvature of such a hypersurface is equivalent to the Monge equation with respect to one of the variables. In the present paper we provide an alternative shorter derivation of this equation by utilizing two invariants discovered by S. Pocchiola. We also investigate Pocchiola’s invariants in the rigid case and give a partial classification of rigid 2-nondegenerate uniformly Levi degenerate of rank 1 hypersurfaces with vanishing CR-curvature.

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DOI : https://doi.org/10.5802/afst.1618
Classification : 32V05,  32V20,  32W20,  35J96,  34A05,  34A26
Mots clés : CR-curvature, tube and rigid hypersurfaces, the Monge–Ampère equation, the Monge equation, Pocchiola’s invariants
@article{AFST_2019_6_28_5_957_0,
     author = {Alexander Isaev},
     title = {Zero {CR-curvature} equations for {Levi} degenerate hypersurfaces via {Pocchiola{\textquoteright}s} invariants},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {957--976},
     publisher = {Universit\'e Paul Sabatier, Toulouse},
     volume = {Ser. 6, 28},
     number = {5},
     year = {2019},
     doi = {10.5802/afst.1618},
     language = {en},
     url = {https://afst.centre-mersenne.org/articles/10.5802/afst.1618/}
}
Alexander Isaev. Zero CR-curvature equations for Levi degenerate hypersurfaces via Pocchiola’s invariants. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 28 (2019) no. 5, pp. 957-976. doi : 10.5802/afst.1618. https://afst.centre-mersenne.org/articles/10.5802/afst.1618/

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